Resultant Velocity of a Kayaker Paddling Across a River
What are the velocities of the kayaker and the current?
A kayaker is paddling across a river at 2.50m/s with a Northeastern direction (45 degrees N of E). A current pulls him with a velocity of 1.25m/s East.
Velocities of the Kayaker and the Current
The kayaker's velocity is 2.50m/s at an angle of 45° (northeast), while the current's velocity is 1.25m/s at an angle of 315° (southeast).
Detailed Explanation of Velocities
When analyzing the motion of the kayaker and the current, it is important to consider their velocities as vectors with both magnitude and direction.
The kayaker's velocity vector can be broken down into horizontal and vertical components. The kayaker is moving at 2.50m/s in a direction 45 degrees north of east which can be represented as (2.50 m/s) (cos(45º) i + sin(45º) j)
After calculation, the kayaker's velocity vector is approximately (1.77 m/s) i + j.
On the other hand, the current's velocity vector is 1.25m/s at an angle of 315 degrees (southeast) which translates to (1.25 m/s) (cos(315º) i + sin(315º) j).
This results in the current's velocity vector being approximately (0.884 m/s) i - j.
The kayaker's resultant velocity is then calculated as the sum of the kayaker's velocity vector and the current's velocity vector.
Therefore, the kayaker's resultant velocity is approximately (2.65 m/s) i + (0.884 m/s) j.
This gives the kayaker a resultant velocity of around 2.80 m/s in a direction of approximately 18.4 degrees north of east.